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P3254 圆桌问题

P3254 圆桌问题

题面

题目链接

解法

较为显然的二分图网络流。

AC代码

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/**
* @file: P3254.cpp
* @author: yaoxi-std
* @url: https://www.luogu.com.cn/problem/P3254
*/
// #pragma GCC optimize ("O2")
// #pragma GCC optimize ("Ofast", "inline", "-ffast-math")
// #pragma GCC target ("avx,sse2,sse3,sse4,mmx")
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define resetIO(x) \
freopen(#x ".in", "r", stdin), freopen(#x ".out", "w", stdout)
#define debug(fmt, ...) \
fprintf(stderr, "[%s:%d] " fmt "\n", __FILE__, __LINE__, ##__VA_ARGS__)
template <class _Tp>
inline _Tp& read(_Tp& x) {
bool sign = false;
char ch = getchar();
long double tmp = 1;
for (; !isdigit(ch); ch = getchar())
sign |= (ch == '-');
for (x = 0; isdigit(ch); ch = getchar())
x = x * 10 + (ch ^ 48);
if (ch == '.')
for (ch = getchar(); isdigit(ch); ch = getchar())
tmp /= 10.0, x += tmp * (ch ^ 48);
return sign ? (x = -x) : x;
}
template <class _Tp>
inline void write(_Tp x) {
if (x < 0)
putchar('-'), x = -x;
if (x > 9)
write(x / 10);
putchar((x % 10) ^ 48);
}
const int MAXN = 550;
const int MAXM = 2e5 + 10;
const int INF = 0x3f3f3f3f3f3f3f3f;
struct Dinic {
struct Edge {
int v, flow;
} edge[MAXM];
int tot = 1, flow = 0;
int head[MAXN], nxt[MAXM], lev[MAXN], cur[MAXN];
void addedge(int u, int v, int flow) {
edge[++tot] = {v, flow};
nxt[tot] = head[u], head[u] = tot;
edge[++tot] = {u, 0};
nxt[tot] = head[v], head[v] = tot;
}
bool bfs(int s, int t) {
fill(lev, lev + MAXN, -1);
queue<int> que;
que.push(s);
lev[s] = 0;
while (!que.empty()) {
int u = que.front();
que.pop();
for (int i = head[u]; i; i = nxt[i]) {
int v = edge[i].v;
if (edge[i].flow && lev[v] == -1) {
lev[v] = lev[u] + 1;
que.push(v);
}
}
}
return lev[t] != -1;
}
int augment(int u, int t, int mx) {
if (u == t || mx == 0)
return mx;
int ret = 0;
for (int &i = cur[u]; i; i = nxt[i]) {
int v = edge[i].v;
if (lev[v] != lev[u] + 1)
continue;
int tmp = augment(v, t, min(mx, edge[i].flow));
mx -= tmp, ret += tmp;
edge[i].flow -= tmp, edge[i ^ 1].flow += tmp;
if (mx == 0)
break;
}
return ret;
}
int maxflow(int s, int t) {
while (bfs(s, t)) {
copy(head, head + MAXN, cur);
flow += augment(s, t, INF);
}
return flow;
}
};
int n, m, s, t, num, r[MAXN], c[MAXN], pt[MAXN][2];
Dinic network;
vector<int> answ[MAXN];
signed main() {
read(m), read(n);
for (int i = 1; i <= m; ++i)
read(r[i]);
for (int i = 1; i <= n; ++i)
read(c[i]);
s = ++num, t = ++num;
for (int i = 1; i <= n; ++i)
pt[i][0] = ++num;
for (int i = 1; i <= m; ++i)
pt[i][1] = ++num;
for (int i = 1; i <= m; ++i)
network.addedge(s, pt[i][1], r[i]);
for (int i = 1; i <= n; ++i) {
network.addedge(pt[i][0], t, c[i]);
for (int j = 1; j <= m; ++j)
network.addedge(pt[j][1], pt[i][0], 1);
}
int sum = 0;
for (int i = 1; i <= n; ++i)
sum += r[i];
if (network.maxflow(s, t) != sum)
return puts("0"), 0;
puts("1");
for (int i = 1; i <= n; ++i) {
for (int j = network.head[pt[i][0]]; j; j = network.nxt[j])
if (network.edge[j].flow && network.edge[j].v > n + 2)
answ[network.edge[j].v - n - 2].push_back(i);
}
for (int i = 1; i <= m; ++i)
for (int j = 0; j < answ[i].size(); ++j)
write(answ[i][j]), putchar(" \n"[j == answ[i].size() - 1]);
return 0;
}